{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T18:08:42Z","timestamp":1788804522446,"version":"build-2803163510"},"reference-count":30,"publisher":"L and H Scientific Publishing, LLC","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JEAM"],"published-print":{"date-parts":[[2027,3,1]]},"abstract":"<jats:p>Motivated by the need to understand the complex interplay between energy dynamics and financial stability, especially in developing countries, this study develops a mathematical model to analyze the impact of economic crises. Examining the XYZR energy model and its financial ramifications in order to manage the energy issues is the aim of this study. When energy is taken into account, the financial system generated to capture the realistic economic crises with critical minimum interest rate. The modified ABC operator is utilized on the newly developed model, converting it into a fractionally ordered to observe the continuous monitoring of the finance system. This type of energy resources and finance system with chaotic behavior is tested using Banach space to look for bounded conclusions, and its basic elements uniqueness. The uniqueness of the constructed system is investigated to determine whether it has a unique solution make consensus for better control. Qualitative analysis derived for steady state position of the XYZR system for validity of the developed system. To confirm its actual state, both qualitative and quantitative analysis is conducted. Utilizing various fractional values, the constructed system's solution is found via Modified ABC scheme, an advanced technique for dependable bounded solution. Additionally, an examination of the developed technique's errors has been carried out to observe the accuracy of the developed results. To observe the actual behaviour and consequences of economic crises, simulations have been built on chaotic finance with critical minimum interest rate including energy sources effects in the developing countries. Determine the true energy state to maximize management after creating a financial plan to minimize losses, then monitor the outcomes with critical minimum interest rate. These kind of studies will be helpful in analyzing the economic crises with energy sources and formulating management plans in light of our confirmed outcomes.<\/jats:p>","DOI":"10.5890\/jeam.2027.03.013","type":"journal-article","created":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T17:41:02Z","timestamp":1788802862000},"page":"241-264","source":"Crossref","is-referenced-by-count":0,"title":["Impact of Economic Crises under Energy Sources with Mathematical Modeling and Control Measures"],"prefix":"10.5890","volume":"15","author":[{"given":"Safdar","family":"Abbas","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Abdul","family":"Ghaffar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aqeel","family":"Ahmad","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kottakkaran Sooppy","family":"Nisar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Muhammad","family":"Farman","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"7015","published-online":{"date-parts":[[2026,9,7]]},"reference":[{"key":"ref1","doi-asserted-by":"crossref","unstructured":"[1] Farman, M., Nisar, K.S., Shehzad, A., Baleanu, D., Amjad, A., and Sultan, F. (2024), Computational analysis and chaos control of the fractional order syphilis disease model through modeling, Ain Shams Engineering Journal, 15(6), 102743.","DOI":"10.1016\/j.asej.2024.102743"},{"key":"ref2","doi-asserted-by":"crossref","unstructured":"[2] Wen, C. and Yang, J. (2019), Complexity evolution of chaotic financial systems based on fractional calculus, Chaos, Solitons & Fractals, 128, 242-251.","DOI":"10.1016\/j.chaos.2019.08.005"},{"key":"ref3","doi-asserted-by":"crossref","unstructured":"[3] Johansyah, M.D., Sambas, A., Qureshi, S., Zheng, S., Abed-Elhameed, T.M., Vaidyanathan, S., and Sulaiman, I.M. (2024), Investigation of the hyperchaos and control in the fractional order financial system with profit margin, Partial Differential Equations in Applied Mathematics, 9, 100612.","DOI":"10.1016\/j.padiff.2023.100612"},{"key":"ref4","doi-asserted-by":"crossref","unstructured":"[4] Johansyah, M.D., Sambas, A., Qureshi, S., Zheng, S., Abed-Elhameed, T.M., Vaidyanathan, S., and Sulaiman, I.M. (2024), Investigation of the hyperchaos and control in the fractional order financial system with profit margin, Partial Differential Equations in Applied Mathematics, 9, 100612.","DOI":"10.1016\/j.padiff.2023.100612"},{"key":"ref5","doi-asserted-by":"crossref","unstructured":"[5] Pan, I., Korre, A., Das, S., and Durucan, S. (2012), Chaos suppression in a fractional order financial system using intelligent regrouping pso based fractional fuzzy control policy in the presence of fractional gaussian noise, Nonlinear Dynamics, 70, 2445-2461.","DOI":"10.1007\/s11071-012-0632-7"},{"key":"ref6","doi-asserted-by":"crossref","unstructured":"[6] Tacha, O.I., Volos, C.K., Kyprianidis, I.M., Stouboulos, I.N., Vaidyanathan, S., and Pham, V.T. (2016), Analysis, adaptive control and circuit simulation of a novel nonlinear finance system, Applied Mathematics and Computation, 276, 200-217.","DOI":"10.1016\/j.amc.2015.12.015"},{"key":"ref7","doi-asserted-by":"crossref","unstructured":"[7] Xiong, P.Y., Jahanshahi, H., Alcaraz, R., Chu, Y.M., G\u00f3mez-Aguilar, J.F., and Alsaadi, F.E. (2021), Spectral entropy analysis and synchronization of a multi-stable fractional-order chaotic system using a novel neural network-based chattering-free sliding mode technique, Chaos, Solitons & Fractals, 144, 110576.","DOI":"10.1016\/j.chaos.2020.110576"},{"key":"ref8","doi-asserted-by":"crossref","unstructured":"[8] Chen, S.B., Jahanshahi, H., Abba, O.A., Sol\u00eds-P\u00e9rez, J.E., Bekiros, S., G\u00f3mez-Aguilar, J.F., Yousefpour, A., and Chu, Y.M. (2020), The effect of market confidence on a financial system from the perspective of fractional calculus: numerical investigation and circuit realization, Chaos, Solitons & Fractals, 140, 110223.","DOI":"10.1016\/j.chaos.2020.110223"},{"key":"ref9","doi-asserted-by":"crossref","unstructured":"[9] Qayyum, M., Ahmad, E., Saeed, S.T., Akg\u00fcl, A., and El Din, S.M. (2024), New solutions of fractional 4d chaotic financial model with optimal control via he-laplace algorithm, Ain Shams Engineering Journal, 15(3), 102503.","DOI":"10.1016\/j.asej.2023.102503"},{"key":"ref10","doi-asserted-by":"crossref","unstructured":"[10] Soukkou, A., Boukabou, A., and Leulmi, S. (2016), Prediction-based feedback control and synchronization algorithm of fractional-order chaotic systems, Nonlinear Dynamics, 85, 2183-2206.","DOI":"10.1007\/s11071-016-2823-0"},{"key":"ref11","doi-asserted-by":"crossref","unstructured":"[11] Rehman, Z.U., Boulaaras, S., Jan, R., Ahmad, I., and Bahramand, S. (2024), Computational analysis of financial system through non-integer derivative, Journal of Computational Science, 75, 102204.","DOI":"10.1016\/j.jocs.2023.102204"},{"key":"ref12","doi-asserted-by":"crossref","unstructured":"[12] Jahanshahi, H., Sajjadi, S.S., Bekiros, S., and Aly, A.A. (2021), On the development of variable-order fractional hyperchaotic economic system with a nonlinear model predictive controller, Chaos, Solitons & Fractals, 144, 110698.","DOI":"10.1016\/j.chaos.2021.110698"},{"key":"ref13","doi-asserted-by":"crossref","unstructured":"[13] Ata, E. and Kiymaz, I.O. (2025), Special functions with general kernel: properties and applications to fractional partial differential equations, International Journal of Mathematics and Computer in Engineering, 3(2), 153-170.","DOI":"10.2478\/ijmce-2025-0013"},{"key":"ref14","doi-asserted-by":"crossref","unstructured":"[14] Ozturk, Z., Bilgil, H., and Sorgun, S. (2024), Fractional SAQ alcohol model: stability analysis and T\u00fcrkiye application, International Journal of Mathematics and Computer in Engineering, 3(2), 125-136.","DOI":"10.2478\/ijmce-2025-0011"},{"key":"ref15","doi-asserted-by":"crossref","unstructured":"[15] Hammouch, Z., Yavuz, M., and \u00d6zdemir, N. (2021), Numerical solutions and synchronization of a variable-order fractional chaotic system, Mathematical Modelling and Numerical Simulation with Applications, 1(1), 11-23.","DOI":"10.53391\/mmnsa.2021.01.002"},{"key":"ref16","doi-asserted-by":"crossref","unstructured":"[16] Xu, Y. and He, Z. (2013), Synchronization of variable-order fractional financial system via active control method, Open Physics, 11(6), 824-835.","DOI":"10.2478\/s11534-013-0237-x"},{"key":"ref17","doi-asserted-by":"crossref","unstructured":"[17] Hou, Y.Y., Lin, M.H., Saberi-Nik, H., and Arya, Y. (2024), Boundary analysis and energy feedback control of fractional-order extended malkus--robbins dynamo system, Chaos, Solitons & Fractals, 183, 114922.","DOI":"10.1016\/j.chaos.2024.114922"},{"key":"ref18","doi-asserted-by":"crossref","unstructured":"[18] Liu, T., Yan, H., Banerjee, S., and Mou, J. (2021), A fractional-order chaotic system with hidden attractor and self-excited attractor and its dsp implementation, Chaos, Solitons & Fractals, 145, 110791.","DOI":"10.1016\/j.chaos.2021.110791"},{"key":"ref19","doi-asserted-by":"crossref","unstructured":"[19] Hussain, S., Bashir, Z., and Malik, M.G. (2024), Chaos analysis of nonlinear variable order fractional hyperchaotic chen system utilizing radial basis function neural network, Cognitive Neurodynamics, 1-25.","DOI":"10.1007\/s11571-024-10118-9"},{"key":"ref20","doi-asserted-by":"crossref","unstructured":"[20] Alain, K.S.T., Azar, A.T., Kengne, R., and Bertrand, F.H. (2020), Stability analysis and robust synchronisation of fractional-order modified colpitts oscillators, International Journal of Automation and Control, 14(1), 52-79.","DOI":"10.1504\/IJAAC.2020.103806"},{"key":"ref21","doi-asserted-by":"crossref","unstructured":"[21] Zhang, G., Qian, P., and Su, Z. (2019), Evolution of fractional-order chaotic economic systems based on non-degenerate equilibrium points, Chaos, Solitons & Fractals, 128, 219-228.","DOI":"10.1016\/j.chaos.2019.08.008"},{"key":"ref22","doi-asserted-by":"crossref","unstructured":"[22] Xue, G., Lin, F., and Qin, B. (2020), Adaptive neural network control of chaotic fractional-order permanent magnet synchronous motors using backstepping technique, Frontiers in Physics, 8, 106.","DOI":"10.3389\/fphy.2020.00106"},{"key":"ref23","doi-asserted-by":"crossref","unstructured":"[23] Caputo, M. and Fabrizio, M. (2021), On the singular kernels for fractional derivatives. Some applications to partial differential equations, Progress in Fractional Differentiation and Applications, 7(2), 1-4.","DOI":"10.18576\/pfda\/070201"},{"key":"ref24","unstructured":"[24] Caputo, M. and Fabrizio, M. (2015), A new definition of fractional derivative without singular kernel, Progress in Fractional Differentiation and Applications, 1(2), 73-85."},{"key":"ref25","doi-asserted-by":"crossref","unstructured":"[25] Al-Refai, M. and Baleanu, D. (2022), On an extension of the operator with Mittag-Leffler kernel, Fractals, 30(5), 2240129.","DOI":"10.1142\/S0218348X22401296"},{"key":"ref26","doi-asserted-by":"crossref","unstructured":"[26] Chawla, R., Deswal, K., Kumar, Devendra, and Baleanu, D. (2022), A novel finite difference based numerical approach for Modified Atangana-Baleanu Caputo derivative.","DOI":"10.3934\/math.2022950"},{"key":"ref27","doi-asserted-by":"crossref","unstructured":"[27] Mohammed, P.O., Srivastava, H.M., Baleanu, D., and Abualnaja, K.M. (2022), Modified fractional difference operators defined using Mittag-Leffler kernels, Symmetry, 14(8), 1519.","DOI":"10.3390\/sym14081519"},{"key":"ref28","unstructured":"[28] Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. (2022), Theory and applications of fractional differential equations, Elsevier, 204."},{"key":"ref29","doi-asserted-by":"crossref","unstructured":"[29] Atangana, A. and Baleanu, D. (2016), New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model, arXiv preprint arXiv:1602.03408.","DOI":"10.2298\/TSCI160111018A"},{"key":"ref30","doi-asserted-by":"crossref","unstructured":"[30] Farman, M., Akg\u00fcl, A., Baleanu, D., Imtiaz, S., and Ahmad, A. (2020), Analysis of fractional order chaotic financial model with minimum interest rate impact, Fractal and Fractional, 4(3), 43.","DOI":"10.3390\/fractalfract4030043"}],"container-title":["Journal of Environmental Accounting and Management"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T17:44:16Z","timestamp":1788803056000},"score":1,"resource":{"primary":{"URL":"https:\/\/lhscientificpublishing.com\/index.php\/jeam\/article\/view\/2510"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,7]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2027,3,1]]}},"URL":"https:\/\/doi.org\/10.5890\/jeam.2027.03.013","relation":{},"ISSN":["2325-6192","2325-6206"],"issn-type":[{"value":"2325-6192","type":"print"},{"value":"2325-6206","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,7]]}}}