Journal of Innovative Applied Mathematics and Computational Sciences http://jiamcs.centre-univ-mila.dz/index.php/jiamcs <p>The Journal of Innovative Applied Mathematics and Computational Sciences (JIAMCS) is an online open access, peer-reviewed semiannual international journal published by<span style="font-size: 0.875rem;"> </span>the Institute of Sciences and Technology, University Center Abdelhafid Boussouf, MILA, ALGERIA.</p> <p>The journal publishes high-quality original research papers from various fields related to applied mathematics, scientific computing, and computer science.</p> <p>In particular, it publishes original papers in the following areas:</p> <ul> <li>Differential equations, (ODE’s, PDE’s, integral equations, difference equations, fractional differential equations)</li> <li>Dynamical systems and bifurcation-chaos theory</li> <li>Fractional calculus</li> <li>Operator's theory</li> <li>Mathematical physics</li> <li>Probability and statistics</li> <li>Mathematical modelling and simulation</li> <li>Numerical analysis</li> <li>Fuzzy logic and systems</li> <li>Lattice theory, number theory and cryptography</li> <li>Modern control theory and practice</li> <li>Mathematical optimization</li> <li>Combinatorial optimisation</li> <li>Computer science</li> <li>Graph theory</li> <li>Bioinformatics</li> <li>Artificial intelligence</li> <li>Pattern recognition</li> <li>Computer vision and image processing</li> <li>Naturel language processing</li> <li>Signal processing</li> <li>Communication theory and network security</li> </ul> <p class="wp-block-columns"><strong>Editor-in-chief: </strong></p> <p>Mohammed Salah Abdelouahab, University Center Abdelhafid Boussouf, Mila, Algeria.</p> <p class="wp-block-columns"><strong>Associate Editors-in-Chief</strong></p> <p><strong>–</strong> Haci Mehmet Baskonus, Harran University, Turkey</p> <p><strong>–</strong> Aissa Boulmerka, University Center Abdelhafid Boussouf, Mila, Algeria</p> <p><strong>– </strong> René Lozi, Université Côte d’Azur, Parc Valrose, Nice, France</p> <p><strong>Published by: </strong></p> <p>Institute of Sciences and Technology, University Center Abdelhafid Boussouf, MILA, ALGERIA.</p> <p><strong>Periodicity: </strong></p> <p>Biannually.</p> Institute of Sciences and Technology, University Center Abdelhafid Boussouf , MILA, ALGERIA. en-US Journal of Innovative Applied Mathematics and Computational Sciences 2773-4196 <ul> <li>Authors keep the rights and guarantee the Journal of Innovative Applied Mathematics and Computational Sciences <em><strong> </strong></em>the right to be the first publication of the document, licensed under a <a href="http://creativecommons.org/licenses/by-nc-nd/4.0/" rel="license">Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License</a> that allows others to share the work with an acknowledgement of authorship and publication in the journal.</li> <li>Authors are allowed and encouraged to spread their work through electronic means using personal or institutional websites (institutional open archives, personal websites or professional and academic networks profiles) once the text has been published.</li> </ul> Non-polynomial Fractional Spline Method for solving Fredholm Integral Equations http://jiamcs.centre-univ-mila.dz/index.php/jiamcs/article/view/v2i3_51 <p> <span class="fontstyle0">A new type of non-polynomial fractional spline function for approximating solutions of Fredholm-integral equations has been presented. For this purpose, we used a new idea of fractional continuity conditions by using the Caputo fractional derivative and the Riemann Liouville fractional integration to generate fractional spline derivatives. Moreover, the convergence analysis is studied with proven theorems. The approach is also well-explained and supported by four computational numerical findings, which show that it is both accurate and simple to apply.</span> </p> Rahel Jaza Faraidun Hamasalh Copyright (c) 2022 Rahel Jaza, Faraidun Hamasalh https://creativecommons.org/licenses/by-nc-nd/4.0 2022-12-14 2022-12-14 2 3 1 14 An approximate solution for the time-fractional diffusion equation http://jiamcs.centre-univ-mila.dz/index.php/jiamcs/article/view/v2i3_46 <p>In this paper, a numerical method based on a finite difference scheme is proposed for solving the time-fractional diffusion equation (TFDE). The TFDE is obtained from the standard diffusion equation by replacing the first-order time derivative with Caputo fractional derivative. At first, we introduce a time discrete scheme. Then, we prove the proposed method is unconditionally stable and the approximate solution converges to the exact solution with order <span id="MathJax-Element-1-Frame" class="MathJax" style="position: relative;" tabindex="0" role="presentation" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x0394;&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi&gt;&amp;#x03B1;&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;"><span id="MathJax-Span-1" class="math" style="width: 5.245em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.208em; height: 0px; font-size: 124%;"><span style="position: absolute; clip: rect(1.616em, 1004.09em, 3.113em, -999.997em); top: -2.704em; left: 0em;"><span id="MathJax-Span-2" class="mrow"><span id="MathJax-Span-3" class="mi" style="font-family: MathJax_Math; font-style: italic;">O</span><span id="MathJax-Span-4" class="mo" style="font-family: MathJax_Main;">(</span><span id="MathJax-Span-5" class="msubsup"><span style="display: inline-block; position: relative; width: 2.653em; height: 0px;"><span style="position: absolute; clip: rect(3.113em, 1001.15em, 4.15em, -999.997em); top: -3.972em; left: 0em;"><span id="MathJax-Span-6" class="texatom"><span id="MathJax-Span-7" class="mrow"><span id="MathJax-Span-8" class="mi" style="font-family: MathJax_Main;">Δ</span><span id="MathJax-Span-9" class="mi" style="font-family: MathJax_Math; font-style: italic;">t</span></span></span></span><span style="position: absolute; top: -4.433em; left: 1.213em;"><span id="MathJax-Span-10" class="texatom"><span id="MathJax-Span-11" class="mrow"><span id="MathJax-Span-12" class="mn" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span id="MathJax-Span-13" class="mo" style="font-size: 70.7%; font-family: MathJax_Main;">−</span><span id="MathJax-Span-14" class="mi" style="font-size: 70.7%; font-family: MathJax_Math; font-style: italic;">α</span></span></span></span></span></span><span id="MathJax-Span-15" class="mo" style="font-family: MathJax_Main;">)</span></span></span></span></span><span class="MJX_Assistive_MathML" role="presentation">O(Δt2−α)</span></span>, where <span id="MathJax-Element-2-Frame" class="MathJax" style="position: relative;" tabindex="0" role="presentation" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x0394;&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/math&gt;"><span id="MathJax-Span-16" class="math" style="width: 1.501em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.213em; height: 0px; font-size: 124%;"><span style="position: absolute; clip: rect(1.846em, 1001.15em, 2.883em, -999.997em); top: -2.704em; left: 0em;"><span id="MathJax-Span-17" class="mrow"><span id="MathJax-Span-18" class="mi" style="font-family: MathJax_Main;">Δ</span><span id="MathJax-Span-19" class="mi" style="font-family: MathJax_Math; font-style: italic;">t</span></span></span></span></span><span class="MJX_Assistive_MathML" role="presentation">Δt</span></span> is the time step size and <span id="MathJax-Element-3-Frame" class="MathJax" style="position: relative;" tabindex="0" role="presentation" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03B1;&lt;/mi&gt;&lt;/math&gt;"><span id="MathJax-Span-20" class="math" style="width: 0.809em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.637em; height: 0px; font-size: 124%;"><span style="position: absolute; clip: rect(1.961em, 1000.58em, 2.768em, -999.997em); top: -2.589em; left: 0em;"><span id="MathJax-Span-21" class="mrow"><span id="MathJax-Span-22" class="mi" style="font-family: MathJax_Math; font-style: italic;">α</span></span></span></span></span><span class="MJX_Assistive_MathML" role="presentation">α</span></span> is the order of Caputo derivative. Finally, some examples are presented to verify the order of convergence and show the application of the present method.</p> Sayed Ali Ahmad Mosavi Copyright (c) 2022 Sayed Ali Ahmad Mosavi https://creativecommons.org/licenses/by-nc-nd/4.0 2022-12-15 2022-12-15 2 3 15 28 Generalized Contraction Theorem in M -Fuzzy Cone Metric Spaces http://jiamcs.centre-univ-mila.dz/index.php/jiamcs/article/view/v2i3_48 <p>This work defines <span id="MathJax-Element-1-Frame" class="MathJax" style="position: relative;" tabindex="0" role="presentation" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;fraktur&quot;&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;"><span id="MathJax-Span-1" class="math" style="width: 1.328em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.04em; height: 0px; font-size: 124%;"><span style="position: absolute; clip: rect(1.731em, 1001.04em, 2.768em, -999.997em); top: -2.589em; left: 0em;"><span id="MathJax-Span-2" class="mrow"><span id="MathJax-Span-3" class="texatom"><span id="MathJax-Span-4" class="mrow"><span id="MathJax-Span-5" class="mi" style="font-family: MathJax_Fraktur;">M</span></span></span></span></span></span></span><span class="MJX_Assistive_MathML" role="presentation">M</span></span>-Fuzzy Cone Metric Space, as a new metric space. It also analyzes possible forms of contractive conditions and groups them accordingly to set up generalized contractive conditions for self-mappings defined over <span id="MathJax-Element-2-Frame" class="MathJax" style="position: relative;" tabindex="0" role="presentation" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;fraktur&quot;&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;"><span id="MathJax-Span-6" class="math" style="width: 1.328em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.04em; height: 0px; font-size: 124%;"><span style="position: absolute; clip: rect(1.731em, 1001.04em, 2.768em, -999.997em); top: -2.589em; left: 0em;"><span id="MathJax-Span-7" class="mrow"><span id="MathJax-Span-8" class="texatom"><span id="MathJax-Span-9" class="mrow"><span id="MathJax-Span-10" class="mi" style="font-family: MathJax_Fraktur;">M</span></span></span></span></span></span></span><span class="MJX_Assistive_MathML" role="presentation">M</span></span>-fuzzy cone metric spaces. We prove the existence of fixed points of these mappings and exhibit the same through a suitable example.</p> Mookiah Suganthi Mathuraiveeran Jeyaraman Avulichikkanan Ramachandran Copyright (c) 2022 Mookiah Suganthi, Mathuraiveeran Jeyaraman, Avulichikkanan Ramachandran https://creativecommons.org/licenses/by-nc-nd/4.0 2022-12-17 2022-12-17 2 3 29 40 Effect of dispersal in two-patch environment with Richards growth on population dynamics http://jiamcs.centre-univ-mila.dz/index.php/jiamcs/article/view/v2i3_47 <p>In this paper, we consider a two-patch model coupled by migration terms, where each patch follows a Richards law. First, we prove the global stability of the model. Second, in the case when the migration rate tends to infinity, the total carrying capacity is given, which in general is different from the sum of the two carrying capacities and depends on the parameters of the growth rate and also on the migration terms. Using the theory of singular perturbations, we give an approximation of the solutions of the system in this case. Finally, we determine the conditions under which fragmentation and migration can lead to a total equilibrium population which might be greater or smaller than the sum of two carrying capacities and we give a complete classification for all possible cases. The total equilibrium population formula for a large migration rate plays an important role in this classification. We show that this choice of local dynamics has an influence on the effect of dispersal. Comparing the dynamics of the total equilibrium population as a function of the migration rate with that of the logistic model, we obtain the same behavior. In particular, we have only three situations that the total equilibrium population can occur: it is always greater than the sum of two carrying capacities, always smaller, and a third case, where the effect of dispersal is beneficial for lower values of the migration rate and detrimental for the higher values. We end by examining the two-patch model where one growth rate is much larger than the second one, we compare the total equilibrium population with the sum of the two carrying capacities.</p> Bilel Elbetch Copyright (c) 2022 Bilel Elbetch https://creativecommons.org/licenses/by-nc-nd/4.0 2022-12-18 2022-12-18 2 3 41 68 Modified projective synchronization of fractional-order hyperchaotic memristor-based Chua’s circuit http://jiamcs.centre-univ-mila.dz/index.php/jiamcs/article/view/v2i3_25 <p data-private="redact" data-wt-guid="d4f0742c-5c9a-4e43-b697-81f5a6f6eb12" data-pm-slice="1 1 []">This paper investigates the modified projective synchronization (MPS) between two hyperchaotic memristor-based Chua circuits modeled by two nonlinear integer-order and fractional-order systems. First, a hyperchaotic memristor-based Chua circuit is suggested, and its dynamics are explored using different tools, including stability theory, phase portraits, Lyapunov exponents, and bifurcation diagrams. Another interesting property of this circuit was the coexistence of attractors and the appearance of mixed-mode oscillations. It has been shown that one can achieve MPS with integer-order and incommensurate fractional-order memristor-based Chua circuits. Finally, examples of numerical simulation are presented, showing that the theoretical results are in good agreement with the numerical ones.</p> Nadjet Boudjerida Mohammed Salah Abdeloahab René Lozi Copyright (c) 2022 Nadjet Boudjerida, Mohammed Salah Abdeloahab, René Lozi https://creativecommons.org/licenses/by-nc-nd/4.0 2022-12-31 2022-12-31 2 3 69 82